First-Principles Study of the Reaction Mechanism in SodiumâOxygen

Article pubs.acs.org/cm

First-Principles Study of the Reaction Mechanism in Sodium−Oxygen Batteries Byungju Lee,† Dong-Hwa Seo,‡ Hee-Dae Lim,† Inchul Park,† Kyu-Young Park,† Jinsoo Kim,† and Kisuk Kang‡,* †

Department of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea Department of Materials Science and Engineering, Research Institute of Advanced Materials, Seoul National University, Seoul 151-742, Republic of Korea

‡

S Supporting Information *

ABSTRACT: Li/O2 battery has the highest theoretical energy density among any battery systems reported to date. However, its poor cycle life and unacceptable energy efficiency from a high charging overpotential have been major limitations. Recently, much higher energy efficiency with low overpotential was reported for a new metal/oxygen system, Na/O2 battery. This finding was unexpected since the general battery mechanism of the Na/O2 system was assumed to be analogous to that of the Li/O2 cell. Furthermore, it implies that fundamentally different kinetics are at work in the two systems. Here, we investigated the reaction mechanisms in the Na/O2 cell using first-principles calculations. In comparative study with the Li/O2 cell, we constructed the phase stability maps of the reaction products of Na/O2 and Li/O2 batteries based on the oxygen partial pressure, which explained why certain phases should be the main discharge products under different operating conditions. From surface calculations of NaO2, Na2O2, and Li2O2 during the oxygen evolution reaction, we also found that the minimum energy barrier for the NaO2 decomposition was substantially lower than that of Li2O2 decomposition on major surfaces providing a hint for low charging overpotential of Na/O2 battery.

1. INTRODUCTION With the high demand for large-scale energy storage devices, it is increasingly important to develop new battery systems with higher energy densities and lower costs. Metal/oxygen batteries are promising new candidates for such applications. Compared with conventional Li-ion batteries (LIBs), metal/oxygen batteries can provide exceptionally higher theoretical energy densities without a use of transition metal element in its reaction. Li/O2 battery,1−5 one of the most extensively studied metal/oxygen systems, can deliver the energy which is ∼10 times higher than those of state-of-art LIBs. However, despite this advantage, Li/O2 batteries have suffered from poor rechargeability and low energy efficiency due to a high polarization during charging (∼60%).2,5−8 The highest efficiency achieved using a nanoporous gold current collector was 70%,9 indicating that 30% of the unused energy was lost in every cycle. Recently, Hartmann et al.10 reported a new metal/ oxygen system based on Na, which was analogous to the Li/O2 system in terms of the cell construction and the expected operating mechanism.10−13 They suggested that sodium superoxide (NaO2) are the main discharge product of the Na/O2 battery as a result of the reaction Na + O2 → NaO2. However, this observation was contrast to the reaction mechanism of Li/O2 system. Previous works on Li/O2 batteries revealed that in the absence of carbonate-based electrolyte, the reaction between lithium and oxygen results in Li2O2 as main discharge product, while LiO2 formation was not detected.2,5−8 © 2014 American Chemical Society

Furthermore, one of the most surprising aspects of the Na/O2 cell was that the polarization was extremely low, enabling an energy efficiency of around 90%, even in the absence of a catalyst. It could be operated with the micrometer size of the discharge products. This is in marked contrast with the Li/O2 system where nanosize Li2O2 discharge products were observed with high overpotential and low energy efficiency. This discrepancy imply that fundamentally different kinetics are at work in two systems. While some of recent theoretical works14,15 have attempted to address the high polarization of the Li/O2 system in the respect of surface reaction kinetics or poor electronic conductivity of Li2O2, to date no theoretical works on Na/O2 battery have been carried out. In the present study, we investigate the reaction mechanism in the Na/O2 cell using first-principles calculations. In this approach, the phase stability maps of discharge products are constructed for reactions in Na/O2 and Li/O2 batteries as a function of oxygen partial pressures to clarify which phase is the main discharge product in various operation conditions. From the calculation of the surface structures of these discharge products, we also estimate the minimum energy barriers for the oxygen evolution reaction (OER) on the major surfaces. In comparison with the results of Li/O2 cell, we discuss on the possible origin Received: September 24, 2013 Revised: January 7, 2014 Published: January 8, 2014 1048

dx.doi.org/10.1021/cm403163c | Chem. Mater. 2014, 26, 1048−1055

Chemistry of Materials

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phases into which the target material transforms in either a reducing or oxidizing environment.25,26,28 For example, Li2O2 can be reduced into Li2O in a lithium-rich environment or oxidized into LiδO2 (δ ∼ 0) in a lithium-deficient environment. The maximum and minimum of the plausible range of the lithium chemical potential are determined by the following reactions:

of low overpotential of Na/O2 cell. This fundamental study on the reaction mechanism is believed to provide insights on the distinct reactions in various metal/oxygen batteries.

2. COMPUTATIONAL METHODOLOGY First-principles calculations were conducted to determine the energies of given states of materials, based on the spin-polarized generalized gradient approximation (GGA) using density functional theory (DFT). Perdew−Burke−Ernzerhof exchange-correlation parametrization was used. We performed the calculations with the Vienna ab initio simulation package (VASP)16 using the projector-augmented wave (PAW)17 method. PAW potentials have shown good predictive capability in battery materials.14,18−22 A plane-wave basis with an energy cutoff of 500 eV was used, and appropriate k-point meshes were chosen to ensure that the total energies converged within 1 meV per formula unit. All structures were fully relaxed. For surface energy calculations, we adopted a slab/vacuum geometry composed of repeating slabs and vacuum layers.14,22−27 A convergence test of the vacuum and slab thicknesses indicated that a vacuum thickness of 10 Å and slab thickness >20 Å were sufficient for convergence within 1 meV/ Å2 for the surface energies. The free energy of a surface was calculated by eq 1: 1 γ= [Gslab − NOμO bulk − NMμM bulk ] (1) 2A where Gslab is the total free energy of the slab supercell, A is the area of the exposed surface, NO and NM are the numbers of oxygen and metal atoms in the slab, respectively, and μObulk and μMbulk are the chemical potentials of oxygen and metal in their bulk phases, respectively. M represents lithium or sodium. Atoms that were positioned at the same crystallographic sites were terminated equally from the top and bottom surfaces to make the two terminations identical; hence, a factor of 1/2 was considered for the two surfaces. The chemical potential of oxygen, μObulk, can be expressed in terms of μMbulk as follows: 1 μOLi 2O2 = GLi 2O2 − μLi Li 2O2 (2) 2 μO Na 2O2 =

1 Na 2O2 G − μ Na Na 2O2 2

(3)

μO NaO2 =

1 NaO2 1 G − μ Na NaO2 2 2

(4)

μLi max ,Li 2O2 = GLi 2O −

2 2

μLi min ,Li 2O2 =

2 2

γNaO = 2

1 1 Li 2O2 → Li + O2 2 2 (9)

μ Na max ,Na 2O2 = GNa 2O −

1 Na 2O2 G 2

1 Na 2O2 + Na → Na 2O 2

(10)

μ Na min ,Na 2O2 = GNa 2O2 − GNaO2

Na 2O2 → Na + NaO2 (11)

where GNa2O, GNa2O, and GNaO2 are the free energies per formula unit of Na2O, Na2O2, and NaO2, respectively. Unlike Li2O2, Na2O2 can be reduced to form the superoxide NaO2; NaO2 is stable under ambient conditions, while LiO2 is thermodynamically unstable. Therefore, the free energy of the superoxide is considered in calculation of the minimum chemical potential of Na in Na2O2. Likewise, for NaO2: μ Na max ,NaO2 = GNa 2O2 − GNaO2

NaO2 + Na → Na 2O2 (12)

μ Na min ,NaO2 = GNaO2 − 2μO0

NaO2 → Na + O2

(13)

The phase stability map was constructed based on the first principles energies of NaOx (or LiOx). The energy is dependent on the oxygen partial pressure, therefore, the energies of NaOx were compared using the fixed oxygen chemical potential and the relative stability was plotted as a function of oxygen chemical potential. The phase stability maps of various metal oxides were constructed as a function of oxygen partial pressure as follows. From eqs 10 and 11, the stability of the Na2O2 phase is found within the range μNamin,Na2O2 ≤ μNa ≤ μNamax,Na2O2, which can be converted to the range of μONa2O2 using eq 3. Similarly, the stability of other phases can be expressed as a function of the chemical potential of oxygen. A phase stability map was drawn from the maximum and minimum limits of the oxygen chemical potential at which the phase was stable. Using eq 14, the phase stability map can be redrawn as a function of oxygen partial pressure.

⎤ 1 ⎡ 1 Gslab − NO·GLi 2O2 − (NLi − NO) ·μLi Li 2O2 ⎥ ⎢ ⎦ ⎣ 2A 2

1 ⎡ 1 Gslab − NO·GNa 2O2 − (NNa − NO) · 2A ⎢⎣ 2 ⎤ μ Na Na 2O2 ⎥ ⎦

1 Li 2O2 G − μO0 2

where GLi2O2 and GLi2O are the free energies per formula unit of Li2O2 and Li2O, respectively, and μO0 is the chemical potential of oxygen gas at 298 K and 1 atm. Similarly, for Na2O2

(5)

γNa O =

1 Li 2O2 + Li → Li 2O 2 (8)

By combining eqs 2, 3, and 4 with eq 1, the surface energies of Li2O2, Na2O2, and NaO2 can be rewritten as γLi O =

1 Li 2O2 G 2

μO(T , P) − μO0 =

(6)

⎛ 1 ⎡ 1 1 ⎞ NaO ⎤ NaO ⎢⎣Gslab − NOG 2 − ⎝⎜NNa − NO⎠⎟μ Na 2 ⎥⎦ 2A 2 2

1 RT ln(PO2) 2

(14)

The surface energy was calculated to estimate the equilibrium morphologies of discharge products. The energies of the seven low-index surfaces; (001), (010), (011), (100), (101), (110), and (111) were calculated for marcasite NaO2 by the vacuum/ slab model, while the energies of the three low-index surfaces; (100), (110), (111) were calculated for pyrite NaO2 due to its

(7)

The plausible range for chemical potentials of Li and Na can be determined by considering the two end members of the 1049



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Figure 1. Bulk structures of (a) marcasite NaO2, (b) pyrite NaO2, (c) Na2O2, and (d) Li2O2. Green, yellow, and red atoms correspond to sodium, lithium, and oxygen, respectively. Dotted lines indicate the oxygen dumbbells in the structure.

higher symmetric space group. The energies of the five lowindex surfaces; (0001), (112̅0), (11̅00), (112̅1), and (11̅01) were considered for both Na2O2 and Li2O2. The reaction free energy of the intermediate steps was calculated as follows: ΔGslab =

1 step ini [Eslab − Eslab − ΔNOμO0 − ΔNM 2 (μMmetal − eU )]

Estep slab

and superoxides.33 The sodium ions in both NaO2 phases occupy octahedral sites, whereas those in Na2O2 occupy prismatic sites. This is in contrast to Li2O2 where the lithium ions occupy both octahedral and prismatic sites in alternating layers. These various metal−oxygen bonding environments are expected to affect the surface properties and the OER mechanism, which will be discussed in detail later. It has not yet been clarified what is the major discharge product for the Na/O2 cell and under what conditions certain discharge products are formed. Hartmann et al.10 observed pyrite NaO2 as the discharge product, while Kim et al.11 and Liu et al.13 reported Na2O2 as the major product. Figure 2

(15)

Eini slab

where is the free energy of the slab at each step, is the initial free energy of the slab, ΔNO and ΔNM are the number of metal and oxygen atoms removed from the surface, and eU is electron energy under the charging potential. If there is no applied potential (U = 0V), then the entire energy step is uphill along the removal of atoms from the surface; therefore, the reaction is not spontaneous. With regard to the oxygen chemical potential, μO0, it is known that the GGA calculation overestimates the binding energy of the oxygen double bond in oxygen gas.29 Different oxygen references have been proposed for correcting overbinding,14,30−32 and there is as yet no consensus regarding the best reference correction. In the present study, the oxygen reference for the Li/O2 cell was chosen from the formation energy of Li2O2 according to the reaction 2Li2O + O2 → 2Li2O2. In the case of the Na/O2 cell, the oxygen reference value was considered from the reaction 2Na2O + O2 → 2Na2O2. However, the difference between the two values was below 0.06 eV per oxygen atom. This difference affected the surface energies at the O2 limit (minimum μLi or μNa cases) by ∼5 meV/Å2, but it did not change the most stable termination or surface. Hence, the oxygen reference for lithium peroxide formation, μ0O = −4.985 eV,14 was used in the entire calculation.

Figure 2. Phase stability map of various lithium/sodium oxides as a function of oxygen chemical potential or oxygen partial pressure. The red line is the oxygen chemical potential where oxygen dissolved in electrolyte is in equilibrium with 1 atm oxygen gas. The blue region is the oxygen chemical potential range under nonequilibrium conditions that can result from fast consumption of O2 in the electrolyte during discharge.

shows that the stable discharge phase is determined by the oxygen partial pressure of the Na/O2 cells in operation. In the figure, the stable sodium/lithium oxides phases are illustrated as a function of oxygen partial pressure. While the marcasite NaO2 was found to be ground state structure at 0K from the calculation, the energy difference with that of pyrite phase was small, 40 meV/f.u., indicating the uncertainty on the room temperature phases in the electrochemical system. Thus, we

3. RESULTS AND DISCUSSION Figure 1 shows the crystal structures of marcasite NaO2, pyrite NaO2, Na2O2, and Li2O2. Although they have different oxygen stackings, the basic unit of each lattice contains the oxygen dumbbell. This is attributed to the strong oxygen−oxygen bond, which is commonly observed in alkali metal peroxides 1050



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plotted both phases of NaO2 in the map. Marcasite and pyrite NaO2 phases were found to be far more stable than Na2O2 phase when the μO is equal to that of the standard condition, T = 298 K and PO2 = 1 atm, as indicated by the red arrow in Figure 2. It shows that NaO2 is likely the first discharge product in Na/O2 reactions at the standard condition. Even under oxygen-deficient conditions, NaO2 seemed to be stable up to PO2 ∼10−8 atm. It was found that Na2O2 phase is stable within range of −0.67 ≤ μO − μO0 ≤ −0.25 eV or −0.67 ≤ μO − μO0 ≤ −0.21 eV in comparison to marcasite and pyrite NaO2 phases, respectively. On the other hand, Na2O is stable only under extremely reducing conditions. The oxygen range in Figure 2 seems to be wider than practical condition, however, it should be noted that 0.1 V of voltage shift corresponds to ∼3 orders of oxygen pressure change. The relationship between cell voltage and oxygen chemical potential is plotted in Supporting Information, which can be easily calculated from eq 2, 3, 4, 14 and Nernst equation. Using similar calculations for the Li/O2 system, our results showed that Li2O2 was the most stable phase at ambient conditions, which was in good agreement with experimental observations.2,8 Li2O was stable under mildly reducing conditions, suggesting that the formation of Li2O is also possible energetically during Li/O2 cell operation. On the other hand, the marcasite LiO2 phase, which is believed to be most stable phase of LiO2,34−36 forms at exceptionally high oxygen partial pressure, ∼40 atm, indicating that it is unlikely to be formed under the normal Li/O2 cell operating conditions. It is contrast to the observation that NaO2 is relatively stable even at low oxygen partial pressure, which is attributed to the larger Na ion that generally forms stronger hybridization with superoxide ion than Li ion case. Nevertheless, it should be noted that the actual environment in the cells may be significantly deviated from the equilibrium, resulting in the formation of kinetically favored phases. For example, in the typical operating conditions of Na/O2 or Li/O2 cells, it may happen that oxygen molecules in the electrolyte are consumed much faster than they are supplied to the electrolyte during discharge; thus, severe oxygen deficiency may occur near the electrode. An oxygen-deficient phase, such as Na2O2 or Li2O, would be generated in such kinetically reducing cases. The surface energies of the NaO2, Na2O2, and Li2O2 were calculated to estimate the equilibrium morphologies of the discharge products and monitor the charging mechanism in the Na/O2 and Li/O2 cells. The most stable termination of each surface was selected by calculating all possible terminations for each surface. (See the computational methodology for surface energy formulation). For example, there are 3 terminations in (100) surface of pyrite NaO2, designated as O2(1)-Na(1), O2(1) and Na(1). The surface energies of each surface are calculated by eq 7 at most reducing condition (eq 12) and most oxidizing condition (eq 13). In this case, termination ‘O2(1)Na(1)’ is most stable at both reducing and oxidizing condition. Similar calculations were conducted for all surfaces of pyrite NaO2, marcasite NaO2, Na2O2, and Li2O2. Detailed information of terminations of each surface is provided in Supporting Information. The calculated surface energies of NaO2, Na2O2, and Li2O2 are summarized in Table 1. The surface energies are shown for both the most oxidizing and reducing conditions because of the possible range of oxygen chemical potential. The surface energy of Li2O2 showed a good agreement with the value reported previously,14 with the slight difference likely due

Table 1. Calculated Surface Energies of the Low-Index Surfaces of Pyrite NaO2, Marcasite NaO2, Na2O2, and Li2O2 under the Most Oxidizing and Reducing Conditions (in meV/Å2) species Pyrite NaO2

Marcasite NaO2

Na2O2

Li2O2

orientation

most oxidizing condition

most reducing condition

(100) (110) (111) (001) (010) (011) (100) (101) (110) (0001) (11̅00) (11̅01) (112̅0) (112̅1) (0001) (11̅00) (11̅01) (112̅0) (1121̅ )

13.5 26.5 18.4 14.5 18.3 14.1 23.5 14.5 21.2 28.4 28.7 32.1 30.6 32.1 31.7 34.7 78.5 42.0 51.5

13.5 26.5 34.1 29.4 22.9 31.6 36.8 15.7 36.7 34.6 34.1 42.3 45.8 46.8 38.8 34.7 82.8 47.1 54.1

to calculation details and the termination strategy (see the Supporting Information). Based on the relative surface energies, the equilibrium shapes of NaO2, Na2O2, and Li2O2 were estimated using the Wulff construction.37 Figure 3 shows the predicted shapes of the discharge products under the most oxidizing and reducing conditions. The pyrite NaO2 particle is mainly composed of (100) surface under reducing conditions (Figure 3b), while the shape was truncated by (110) and (111) surfaces in oxidizing conditions (Figure 3a). A recent experimental study indicated that the NaO2 crystallite had a cubic-like morphology (Figure 3c) in pyrite phase,10,38 corresponding well to our calculated Wulff shape under reducing conditions. It may indicate that the experimental condition of the Na/O2 cell resembled the oxygen-deficient condition. We expect that the effectively reducing condition can occur when the rate of oxygen consumption in the electrolyte is significantly higher compared to its supply during discharge. Thus, it is also possible that the Na2O2 is formed when severely oxygen-deficient environment is imposed under practical experimental conditions. Depending on the surface area of the air electrode and the amount of the electrolyte of the cell, the rate of oxygen consumption and the supply might vary. It is noteworthy that Hartmann et al.,10 who observed NaO2 discharge product, used macro gas diffusion layer (GDL) as an air-electrode, while Kim et al.11 and Liu et al.,13 who observed Na2O2, used high surface area carbon in their airelectrode. The marcasite NaO2 particle shape was mainly composed of the (010) and (101) surfaces under reducing conditions (Figure 3e), and it was truncated by other surfaces, i.e., (011), (001), and (111) under oxidizing conditions (Figure 3d). The crystal shape of Na2O2 looks more complex and is composed of various surfaces such as (0001), (112̅0), (11̅00), and (110̅ 1) (Figure 3(f, g)). It contrasts with the shape of Li2O2, which was mainly composed of two surfaces; (0001) and (11̅00) (Figure 3(h, i)). These were reported as main surfaces in previous theoretical works on Li2O2.30,39 1051



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Figure 3. Wulff shapes of (a), (b) pyrite NaO2, (d), (e) marcasite NaO2, (f), (g) Na2O2, and (h), (i) Li2O2 during the OER on the corresponding surfaces. The left sides (a), (d), and (f) are for the most oxidizing conditions, and the right sides (b), (e), and (g) are for the most reducing conditions of each material. (c) SEM image of the pyrite NaO2 crystallite in the discharged Na/O2 cell. The calculated minimum energy barrier of OER for all the surfaces are represented as a colored map in the Wulff shape of each material. Major surfaces of the Na discharge products are comprised of the surfaces with low OER barriers. Reproduced with permission from ref 10. Copyright 2013 Nature Publishing Group.

chemical intermediate state, while the other effects were neglected. To visualize the total minimum energy barrier required for the reaction, the energy profiles of intermediate steps at each surface were plotted along the reaction coordinate. The energy profiles of the two most stable surfaces of each material are shown in Figure 4. The profiles of other surfaces are provided in Supporting Information. As shown in Figure 4a−d, the OER barrier is generally lower for Na/O2 systems. While the results for Li2O2 in Figure 4g and h were in good agreement with the previous work,14 the minimum energy barrier of the NaO2 decomposition reaction was notably lower for both pyrite and marcasite phases. The minimum energy barrier required to decompose NaO2 phases were as low as 0.1−0.8 eV, which contrasts with 0.9−2.0 eV for that of Li2O2 on major surfaces. Also, the decomposition of Na2O2 required 0.8−0.9 eV, which is still lower than that of Li2O2 even though it is relatively higher than those of NaO2. Note that the overpotential of decomposition reaction, which is calculated from electrochemical step only, is 0.02−0.15 V for NaO2, 0.07− 0.21 V for Na2O2 and 0.17−0.21 V for Li2O2 at major surfaces. The overpotential values of decomposing NaO2 is lower than reported value of decomposing Li2O2 in various mechanisms. The overpotential of the topotactic decomposition of Li2O2 via LiO2-like phase reported by Kang et al.35 was ∼0.34 V, and that of Li2O2 decomposition at surface defects32 was 0.15−0.19 V. During OER, oxygen removal step significantly affected the

Given the surface morphologies of the discharge products, we investigated the OER mechanism occurring at the surface. During the OER, oxygen or metal atoms leave the surface upon charging. There are two possible sequences for the decomposition reaction; whether the metal is extracted first or the oxygen molecule evolves first. These steps can be expressed as MxOy → Mx − 1Oy + M+ + e−

(16)

and MxOy → MxOy − 2 + O2

(17)

where MxOy is the formula for the surface structures of NaO2, Na2O2, and Li2O2, and M represents Na or Li. The energies of the intermediate steps of the OER were considered by removing metal or oxygen molecules from the surface until all the atoms in the surface of the unit cell were consumed. As the final termination is identical to the initial termination when the unit formula is removed from the surface, the entire decomposition procedure could be described by considering one unit cell. Ideally, the OER occurs under the equilibrium potential, U = 2.41 V for pyrite NaO2, U = 2.45 V for marcasite NaO2, U = 2.21 V for Na2O2, and U = 2.82 V for Li2O2 in eq 15. Due to the unstable intermediate steps during the decomposition, additional potential must be applied to make the reaction occur. Note that the minimum energy barrier calculated here only included a contribution from the unstable 1052



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Figure 4. OER energy profile of the surfaces in pyrite NaO2, marcasite NaO2, Na2O2, and Li2O2. The surfaces of interest were selected: (a) (110) surface of pyrite NaO2, (b) (100) surface of pyrite NaO2, (c) (101) surface of marcasite NaO2, (d) (010) surface of marcasite NaO2, (e) (0001) surface of Na2O2, (f) (110̅ 0) surface of Na2O2, (g) (0001) surface of Li2O2, and (h) (110̅ 0) surface of Li2O2. The most favorable reaction paths are shown. The chemical steps are shown in red.

total minimum energy barrier (denoted as red steps in the figure) even though these steps were not electrochemical

reaction. While it can be debatable whether the chemical evolution of the O2 would contributed to the overpotential, we 1053



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4. CONCLUSIONS The reaction mechanism in Na/O2 cell was investigated using first-principles calculations and compared with that of Li/O2 cell. We found that the discharge products of the Na/O2 and Li/O2 cells are NaO2 and Li2O2, respectively in standard conditions, even though it can vary depending on the effective atmosphere in the experiment. Surface calculations of discharge phases revealed the equilibrium shapes of the particles, which are in an excellent agreement with the experimental observation. Furthermore, the simulation of OERs on major surfaces of discharge products indicated that the NaO2 decomposition reaction required less minimum energy barrier than those of Li2O2 decomposition providing a hint for a low overpotential of Na/O2 cell compared to Li/O2 cell. While the presence of different electrolytes can affect on the energetics and equilibrium morphologies of the discharge products, this study provides the basic fundamental properties of various discharge products and broaden our understanding on the metal/oxygen batteries.

believe that the sluggish reaction from chemical steps would indirectly result in the polarization during charge even though the overpotential would not indirectly scale with the barrier energy. Moreover, these chemical steps formed substantial barriers in almost all decomposition reactions as shown in Figure 4. It is interesting that it is comparable to well-known water (H2O) splitting reaction kinetics, where oxygen evolution reaction requires high energy barrier in oxygen bonding formation due to four electrons transfer.40 Nevertheless, these steps become comparatively smaller in NaO2 phases than Li2O2. We attribute this in part to differences in oxygen contents in each phases. In oxygen-rich NaO2 phases, the metal−oxygen (M-O) bonding in the lattice is likely to be weaker than in oxygen-poor Li2O2. There are nine metal ions around one peroxide ion (O22−) in peroxide phase, while superoxide ion (O2−) is surrounded by six atoms in superoxide phase. This strong M-O bond in the Li2O2 crystal lattice causes the O2-escaping step from the crystal to be less favorable. This is further supported by the less stable chemical step observed for the Na2O2 phase than that for NaO2 phases. Oxygen-poor Na2O2 is likely to hold oxygen more strongly in the crystal lattice, leading to a higher energy cost for oxygen evolution. Distinct metal−oxygen bondings in different crystal sites are also partially responsible for different OER barriers. We observed that the volume of prismatic MO6 was significantly smaller than that of octahedral MO6 for both the Na and Li phases, with substantially shorter M-O distances. While it is rather counterintuitive since the interstitial volume is generally bigger in prismatic sites than octahedral sites,41 it indicates that the M-O bond is likely stronger in the prismatic configuration. The higher minimum energy barrier of Na2O2 decomposition than that of NaO2 may be related to the prismatic NaO6 in Na2O2. The stronger binding of Na and oxygen in Na2O2 with purely prismatic configuration is expected to be more difficult to break than those in NaO2 with octahedral configurations. In Li2O2, there are both octahedral and prismatic configurations for Li. Since both configurations need to be broken for full decomposition reaction, the rate limiting would occur at prismatic LiO6. Compact LiO6 prisms would bind the oxygen strongly, resulting in a high minimum energy barrier for decomposition. It is worthwhile to note that the low overpotential was observed for the NaO2 decomposition reaction by Hartmann et al.,10 while relatively higher overpotential was experimentally observed for that of Na2O2.13 Electrical conductivities of discharge products may influence the overall overpotential of Na/O2 cell and Li/O2 cell in addition to the minimum energy barrier for OER. Many groups15,42,43 studied the charge transport mechanism and the conductivity of Li2O2 and suspected that poor conductivity of Li2O2 can be culprit for high overpotential in Li/O2 cell. In this respect, we compared bandgaps of discharge products by HSE06 hybrid functional calculation. Bandgaps of pyrite NaO2, marcasite NaO2, Na2O2, and Li2O2 were found to be 1.09 eV, 1.11 eV, 2.94 eV, and 4.60 eV, respectively, from the density of states for each materials (Supporting Information). We found that bandgaps of sodium phases are generally lower than Li2O2 possibly resulting in better electronic conductivity. However, the bandgaps are still too high to account for the exceptionally low overpotential of Na/O2 cells, even though the electronic structure of off-stoichiometric products such as NaO2‑δ and Na1‑δO2 should be investigated further to confirm this.

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ASSOCIATED CONTENT

* Supporting Information S

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by (i) the Supercpmputing Center/ Korea Institute of Science and Technology Information with supercomputing resources including technical support KSC2012-C2-51, (ii) the National Research Foundation of Korea Grant funded by the Korean Government (MEST) (NRF2009-0094219), and (iii) the Human Resources Development program (20124010203320) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy.

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REFERENCES

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